This relates to graphics processing and particularly to progressive refinement rendering for volume ray tracing.
Many rendering techniques require the taking of multiple “samples” for super-sampling, for Monte-Carlo integration of direct or indirect lighting effects in the context of photo-realistic rendering, or for volumetric integration of opacity and emittance along a ray in the context of volume rendering. Generally the more samples the better the accuracy of the result, but the higher the rendering time. Despite faster hardware and more efficient algorithms, it is not possible, in particular for interactive applications, to compute as many samples as desired in the time available for each frame.
The state of the art method to attack this problem is to perform “progressive refinement” rendering. Rather than computing all samples in every frame, progressive refinement takes only as many samples per frame as can be afforded to maintain interactivity. This approach trades image quality for interactivity and then “fixes” the reduced image quality by merging successive frames' partial results, typically by accumulating/averaging those frames' pixel values.
This form of progressive refinement generally works well for all sorts of Monte-Carlo integrations where individual samples are independent (and can thus be averaged in multiple batches). One important algorithm where it does not work well, however, is volume integration.
In volume rendering or volume integration, a volume is modelled as a medium that can emit, transmit and absorb light. A volume rendering integral may be solved by ray casting. Since the multiple samples along each ray are not independent in volume rendering, averaging multiple individually integrated rays' results (with few samples each) is not the same as integrating a single ray with many samples. Consequently, progressive refinement in the context of volume rendering will generally not converge to the same image as a reference technique with a large number of samples all shot in a single frame.